asymptotes are lines that our function gets close to as we approach particular value(s) in the domain. there are three types: vertical, horizontal and oblique. you should look these up in a google search or something. you need to know what asymptotes are and how to find them if you are to answer problems of this nature.

What is the asymptote for g(x)=log(5)2x? I cannot get this to sink in.

start with an easier question: what is the asymptote for log(x)?

what is the domain of the logarithm graph, that is, the domain of log(x)?

do logarithm graphs have vertical or horizontal asymptotes, both maybe?

these are things you must know in order to tackle these problems. you can't find something if you don't know what you are looking for. a bit philosophical i know, but provide the asnwers to the above questions, if you can, and we will take it from there